The present invention relates to a method of enriching a gaseous effluent in acid compounds, which comprises the following stages: feeding into a contactor a feed gas comprising acid compounds and a composition comprising at least two liquid phases non-miscible with one another, including an aqueous phase, at least one amphiphilic compound and at least one mixture of promoters, establishing in said contactor predetermined pressure and temperature conditions for the formation of hydrates consisting of water, promoters and acid compounds, carrying the hydrates dispersed in the phase non-miscible in the aqueous phase through pumping to a hydrate dissociation drum, establishing in the drum the hydrate dissociation conditions, discharging the gas resulting from the dissociation enriched in acid compounds in relation to the feed gas.